The Annals of Probability

Necessary and Sufficient Lifetime Conditions for Normed Convergence of Critical Age-Dependent Processes with Infinite Variance

Martin I. Goldstein and Fred M. Hoppe

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Abstract

The critical age-dependent branching process with offspring p.g.f. of the form $f(s) = s + (1 - s)^{1 + \alpha}L(1 - s), 0 < \alpha \leq 1, L$ slowly varying at 0, is investigated. We generalize Kesten's unpublished necessary condition to establish N.A.S.C. on the tail of the lifetime distribution for existence of a nondegenerate normalized conditioned limit law and pose several related questions.

Article information

Source
Ann. Probab., Volume 9, Number 3 (1981), 490-497.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994421

Digital Object Identifier
doi:10.1214/aop/1176994421

Mathematical Reviews number (MathSciNet)
MR614633

Zentralblatt MATH identifier
0461.60093

JSTOR
links.jstor.org

Subjects
Primary: 60K99: None of the above, but in this section
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
Critical age-dependent branching process regular variation conditional limit law lifetime distribution

Citation

Goldstein, Martin I.; Hoppe, Fred M. Necessary and Sufficient Lifetime Conditions for Normed Convergence of Critical Age-Dependent Processes with Infinite Variance. Ann. Probab. 9 (1981), no. 3, 490--497. doi:10.1214/aop/1176994421. https://projecteuclid.org/euclid.aop/1176994421


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